If trim is manual, why on earth would you trim nose-down and hold the stick hard back?
Good question. I wouldn't. Do we know that the stick was "hard back"? Not yet anyway.
If they had noticed the trim they would have noticed it was doing as asked - they were asking for full nose-up.
Not necessarily. I believe that they forgot, or never really knew, that back stick would trim them up into a stall. I'm not convinced that the PF realized he was pulling back.